1. Field of the Invention
The present invention relates generally to the field of electrical field logging of oil wells. More specifically, the present invention is a method of obtaining a measure of a parameter of a formation using a real component of an electrically induced signal in a formation.
2. Description of the Related Art
It is important to the oil and gas industry to know the nature and characteristics of the various sub-surface formations penetrated by a borehole because the mere creation of a borehole (typically by drilling) usually does not provide sufficient information concerning the existence, depth location, quantity, etc., of oil and gas trapped in the formations. Various electrical techniques have been employed in the past to determine this information about the formations. One such technique commonly used is induction logging. Induction logging measures the resistivity (or its inverse, conductivity) of the formation by first inducing eddy currents to flow in the formations in response to a transmitter signal, and then measuring a phase component signal in a receiver signal generated by the presence of the eddy currents. Variations in the magnitude of the eddy currents in response to variations in formation conductivity are reflected as variations in the receiver signal. Thus, in general, the magnitude of the in-phase component (the component that is in-phase with the transmitter signal) is indicative of the conductivity of the formation.
The physical principles of electromagnetic induction resistivity well logging are described, for example, in H. G. Doll, Introduction to Induction Logging and Application to Logging of Wells Drilled with Oil-Based Mud, Journal of Petroleum Technology, vol. 1, p. 148, Society of Petroleum Engineers, Richardson, Tex. (1949). Many improvements and modifications to electromagnetic induction resistivity instruments have been devised since publication of the Doll reference, supra. Examples of such modifications and improvements can be found, for example, in U.S. Pat. Nos. 4,837,517; 5,157,605 issued to Chandler et al.; and U.S. Pat. No. 5,452,761 issued to Beard et al.
The basic theory of induction logging instruments for evaluation of formation resistivity is taught in U.S. Pat. No. 3,147,429 to Moran and is summarized here. Shown in FIG. 1 are exemplary transmitter coil and receiver coil with a distance L between them. The transmitter has a product At of the cross-sectional area times the number of coils. The corresponding product for the receiver coil is Ar. The propagation constant k is given by:k=√{square root over (jωσμ)}  (1)where j is the square root of −1, ω is the angular frequency of the signal, σ is the formation conductivity and μ is the permeability of the medium. Eqn. (1) can be rewritten as
                    γ        =                              1            +            j                    δ                                    (        2        )            where δ denotes the “skin depth” in the medium and is given by
                    δ        =                              2            ωσμ                                              (        3        )            
When a current I is passed through the transmitter, eddy currents are induced in the formation which in turn induce a magnetic field and eddy currents in the receiver. The total receiver voltage V is given by the expression:
                    V        =                              -            jω                    ⁢                                          ⁢          I          ⁢                                                                      μ                  ⁢                                                                          ⁢                                      A                    T                                    ⁢                                      A                    R                                                                    2                  ⁢                  π                  ⁢                                                                          ⁢                                      L                    3                                                              ⁡                              [                                                                                                    1                        -                                                                                                            (                                                              j                                ⁢                                                                                                                                  ⁢                                γ                                ⁢                                                                                                                                  ⁢                                L                                                            )                                                        2                                                    2                                                -                                                                                                            (                                                              j                                ⁢                                                                                                                                  ⁢                                γ                                ⁢                                                                                                                                  ⁢                                L                                                            )                                                        3                                                    3                                                -                                                                                                                                                                                                      -                                                                                                                            (                                                                      j                                    ⁢                                                                                                                                                  ⁢                                    γ                                    ⁢                                                                                                                                                  ⁢                                    L                                                                    )                                                                4                                                            8                                                                                -                                                                                                                    (                                                                  jγ                                  ⁢                                                                                                                                          ⁢                                  L                                                                )                                                            5                                                        30                                                    -                          …                                                ⁢                                                                                                                                                                      ]                                      .                                              (        4        )            
Separating into real and imaginary parts gives the real and imaginary parts Vr and Vx (in-phase and quadrature components) as
                                          V            r                    =                                                                      σω                  2                                ⁢                                  μ                  2                                ⁢                                  A                  t                                ⁢                                  A                  r                                                            4                ⁢                π                ⁢                                                                  ⁢                L                                      [                          1              -                                                2                  3                                ⁢                                  (                                      L                    δ                                    )                                            +                                                2                  15                                ⁢                                                      (                                          L                      δ                                        )                                    2                                            -              …                        ⁢                                                  ]                          ⁢                                  ⁢        and                            (        5        )                                          V          x                =                                            σ              ⁢                                                          ⁢              ωμ              ⁢                                                          ⁢                              IA                t                            ⁢                              A                r                                                    4              ⁢              π              ⁢                                                          ⁢              L                                ⁡                      [                                          -                1                            +                                                2                  3                                ⁢                                                      (                                          L                      δ                                        )                                    3                                            -                                                1                  2                                ⁢                                                      (                                          L                      δ                                        )                                    4                                            +                                                2                  15                                ⁢                                                      (                                          L                      δ                                        )                                    5                                                      ]                                              (        6        )            It should be pointed out that the quadrature component of voltage is equivalent to the real component of the magnetic field.
A typical electrical resistivity-measuring instrument is an electromagnetic induction military well logging instrument such as described in U.S. Pat. No. 5,452,761 issued to Beard et al. The induction logging instrument described in the Beard '761 patent includes a number of receiver coils spaced at various axial distances from a transmitter coil. Alternating current is passed through the transmitter coil, which induces alternating electromagnetic fields in the earth formations. Voltages, or measurements, are induced in the receiver coils as a result of electromagnetic induction phenomena related to the alternating electromagnetic fields. A continuous record of the voltages forms curves, which are also referred to as induction logs. Induction instruments that are comprised of multiple sets of receiver coils are referred to as multi-array induction instruments. Every set of receiver coils together with the transmitter is called a subarray. A multi-array induction tool consists of numerous subarrays and acquires measurements with all the subarrays.
Voltages induced in the axially more distal receiver coils are the result of electromagnetic induction phenomena occurring in a larger volume surrounding the instrument, and the voltages induced in the axially proximal receiver coils are the result of induction phenomena occurring more proximal to the instrument. Therefore, different receiver coils see a formation layer boundary with different shoulder-bed contributions, or shoulder-bed effects. The longer-spaced receiver coils see the formation layer boundary at further distance from the borehole than the shorter-spaced receiver coils do. As a result, the logs of longer-spaced receiver coils have longer shoulder-bed effects than the logs of shorter-spaced receiver coils. The logs of all the receiver coils form a certain pattern.
A newly developed induction instrument comprises three mutually orthogonal transmitter-receiver arrays. Such a configuration makes it possible to determine both horizontal and vertical resistivities for an anisotropic formation in vertical, deviated, and horizontal boreholes. A description of the tool can be found in U.S. Pat. No. 6,147,496 to Strack, et al. The transmitters induce currents in three mutually perpendicular spatial directions and the receivers measure the corresponding magnetic fields (Hxx, Hyy, and Hzz). In this nomenclature of the field responses, the first index indicates the direction of the transmitter, the second index denotes the receiver direction. As an example, Hzz is the magnetic field induced by a z-direction transmitter coil and measured by a z-directed receiver. The z-direction is parallel to the borehole. Included in Strack is a teaching of how measurements made at two frequencies can be combined to give the resistivity of the earth formation away from the borehole while avoiding the effects of possible invasion of borehole fluids into the formation. Other methods for processing of multicomponent induction data use a frequency focusing method in which measurements are made at several frequencies. Examples of such methods are given in U.S. Pat. No. 6,574,562 of Tabarovsky et al.
The imaginary component of the magnetic field is commonly used in the inversion processing methods identified above. This corresponds to the real part of the voltage noted above in eqn. (5). The real component of a single frequency magnetic field measurement has similar properties to the imaginary component of a dual frequency (or multi-frequency) magnetic field measurement. So far, industry has not used the real component of magnetic field from induction logging data in data processing. The present invention is directed towards the use of the real component of the magnetic field for determination of anisotropic formation resistivity.